Power tracking, thermal management and system efficiency optimization are three key issues of ensuring high performance and long life time for a SOFC system from the view of practical application. In this paper, a novel control strategy is proposed to cooperatively manage the three competitive issues by maintaining thermal constraints and optimizing system efficiency while conducting fast load tracking. Firstly, a validated high fidelity SOFC system model incorporating a one-dimensional stack model is constructed according to physical laws and chemical kinetics. With this model, we have conducted in-depth system analysis and calculated optimal operating points (OOPS) for different power outputs, and then found the mechanism for efficiency optimization. By transient analysis of OOPS based power switching process, a thermo-electric decoupling method and systematic thermos-electrical cooperative controlling strategy are proposed. The control strategy includes two sub-controllers, one is an OOPS based feed-forward controller for thermal management, and the other is Takagi-Sugeno (TS) fuzzy model based constrained generalized predictive control (CGPC) controller for power tracking, input constraint handling and fuel starvation prevention. By applying this control strategy, the system efficiency can be improved to 43-53% during fast power tracking and temperature constraining can be guaranteed. (C) 2018 Elsevier Ltd. All rights reserved.